Using probabilistic methods we derive a complete characterization of the sub-class of HJM models that guarantee positive interest rates. Explicit formulas are given for the conditional zero coupon bond prices in terms of the initial yield curve data and a fundamental family of martingales. It is...

This article describes a new approach to compute values and sensitivities of synthetic collateralized debt obligation (CDO) tranches in the market-standard, single-factor, Gaussian copula model with base correlation. We introduce a novel decomposition of the conditional expected capped portfolio...